Calculating intermodulation products and intercept points for circuit distortion analysis

Abstract

A pertubative approach based on the Born approximation resolves weakly nonlinear circuit models without requiring explicit high-order device derivatives. Convergence properties and the relation to Volterra series are discussed. According to the disclosed methods, second and third order intermodulation products (IM2, IM3) and intercept points (IP2, IP3) can be calculated by second and third order Born approximations under weakly nonlinear conditions. A diagrammatic representation of nonlinear interactions is presented. Using this diagrammatic technique, both Volterra series and Born approximations can be constructed in a systematic way. The method is generalized to calculate other high-order nonlinear effects such as IMn (nth order intermodulation product) and IPn (nth order intermodulation intercept point). In general, the equations are developed in harmonic form and can be implemented in both time and frequency domains for analog and RF circuits.

Description

BACKGROUND OF THE INVENTION[0001]The present invention relates to the analysis of circuits generally and more particularly to the distortion analysis of analog and RF (Radio Frequency) circuits by calculating intermodulation products and intercept points.[0002]Second and third order intermodulation intercept points (IP2 and IP3) are critical design specifications for circuit nonlinearity and distortion. A rapid yet accurate method to compute IP2 / IP3 is of great importance in complex RF and analog designs. Conventional computer-aided-design solutions for measuring IP2 / IP3 are typically based on multi-tone simulations. For a circuit with a DC (Direct Current) operating point such as a LNA (Low Noise Amplifier), a two-tone simulation is performed at two RF input frequencies ω1 and ω2 (usually closely spaced). When the RF power level is low enough, signals at frequencies ω1−ω2 and 2ω1−ω2 are dominated by second and third order nonlinear effects respectively, and higher order contributio...

AI Technical Summary

Benefits of technology

This approach simplifies the calculation of IP2 and IP3, providing accurate results with reduced computational complexity and efficiency, comparable to multi-tone simulations but with lower overhead, and can be implemented in both time and frequency domains.

Problems solved by technology

Furthermore, a multi-tone simulation is generally inefficient for IP2 / IP3 measurements because, in addition to IM2 and IM3 harmonics, this approach also resolves other irrelevant frequencies to all nonlinear orders.

This additional overhead can be very expensive in large designs with thousands of transistors.

However, this approach requires second and higher order derivatives of nonlinear devices.

This limits the application of Volterra series in many circuit simulations since most device models don't provide derivatives higher than first order.

Also, as the order of Volterra series increases, the complexity of tracking the polynomials grows substantially, and the implementation becomes more and more complicated.

Images